Solve the problem. determine which of the following sets is a subspace of pn for an appropriate value of n. a: all polynomials of the form p(t) = a + bt2, where a and b are in ℛ b: all polynomials of degree exactly 4, with real coefficients c: all polynomials of degree at most 4, with positive coefficients

Only and form subspaces of and , respectively.

does not form a subspace because it does not contain the zero vector.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).